Question

Consider the sets U = {a,b,c,d,e,f,g}, A = {b,c,d,e) and B = {a, c, g}. Find A' and B' and then verify that (AUB)' = A'B'.

Answer 1

Step-by-step explanation:

A'=U-A={a,b,c,d,e,f,g} - {b,c,d,e}

A' ={a,f,g}

B'= U-B={a,b,c,d,e,f,g} - {a,c,g}

B'={b,d,e,f}

L.H.S:-

(AUB)'= U- (AUB)

={a,b,c,d,e,f,g} - ({b,c,d,e} U { a,c,g})

={a,b,c,d,e,f,g} - {a,b,c,d,e,g}

(AUB)' ={f}

R.H.S:-

A'nB'= {a,f,g} n {b,d,e,f}

= {f}

L.H.S=R.H.S